Recently the idea of moiré bilayer[1]}, [2]} was introduced by us to simulate “spin” physics and realize quantum spin liquid (QSL)[3]}, [4]}, [5]} phases using the layer pseudospin. Similar to the quantum Hall bilayer[6]}, [7]}, [8]}, we consider a bilayer system where two layers are coupled through inter-layer repulsion without inter-layer tunneling (see Fig. REF ). Thus the total charge of each layer is separately conserved. If we label the charge of the two layers as \(Q_t\)  and \(Q_b\)  respectively, we can define two conserved quantum numbers: \(Q=Q_t+Q_b\)  and \(P_z=\frac{1}{2}(Q_t-Q_b)\) . We can view \(Q\)  as the total charge, then \(P_z\)  is a pseudospin and its transport can be conveniently probed by electrically counter-flow measurement[1]}. We also need the inter-layer distance \(d\)  to be much smaller than the intra-layer lattice constant \(a_M\)  so that the inter-layer repulsion is comparable to the intra-layer repulsion. To achieve that, it is natural to build up a bilayer using moire superlattices based on graphene[10]}, [11]}, [12]}, [13]}, [11]}, [15]}, [16]}, [17]}, [18]}, [19]}, [20]}, [21]}, [22]}, [23]} or transition metal dichalcogenides (TMD)[24]}, [25]}, [26]}, [27]}, [28]}, [29]}, [30]}. Here we will focus on TMD moiré superlattice in which Mott physics and anti-ferromagnetic spin coupling have been well studied in single moiré layer[24]}, [25]}, [26]}, [29]}, [30]}.
